Solve 25x^(2)-81 - ScanMath

Question

25 x^{2} - 81

Factor the expression

(5 x - 9) (5 x + 9)

Evaluate

25 x^{2} - 81

Rewrite the expression in exponential form

(5 x)^{2} - 9^{2}

Solution

(5 x - 9) (5 x + 9)

Show Solution

x_{1} = - \frac{9}{5}, x_{2} = \frac{9}{5}

Alternative Form

x_{1} = - 1.8, x_{2} = 1.8

Evaluate

25 x^{2} - 81

To find the roots of the expression,set the expression equal to 0

25 x^{2} - 81 = 0

Move the constant to the right-hand side and change its sign

25 x^{2} = 0 + 81

Removing 0 doesn't change the value,so remove it from the expression

25 x^{2} = 81

Divide both sides

\frac{25 x ^{2}}{25} = \frac{81}{25}

Divide the numbers

x^{2} = \frac{81}{25}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{81}{25}

Simplify the expression

More Steps

Evaluate

\frac{81}{25}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{81}{25}

Simplify the radical expression

More Steps

Evaluate

81

Write the number in exponential form with the base of 9

9^{2}

Reduce the index of the radical and exponent with 2

9

\frac{9}{25}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{9}{5}

x = \pm \frac{9}{5}

Separate the equation into 2 possible cases

x = \frac{9}{5} x = - \frac{9}{5}

Solution

x_{1} = - \frac{9}{5}, x_{2} = \frac{9}{5}

Alternative Form

x_{1} = - 1.8, x_{2} = 1.8

Show Solution